1. Field of the Invention
The object of the present invention is a method for gradually deforming an initial distribution of objects of geologic nature, formed by simulation of a stochastic model of object type, from measurements or observations, so as to best adapt it to imposed physical constraints of, for example, a hydrodynamic type.
2. Description of the Prior Art
French Patent 2,780,798 filed by the assignee describes a method for gradually deforming a stochastic model (of Gaussian type or similar) of a heterogeneous medium such as an underground zone, constrained by a series of parameters relative to the structure of the medium. This method comprises drawing a number p of independent realizations (or representations) of the model or of at least part of the selected medium model from all of the possible realizations, and one or more iterative stages of gradual deformation of the model by carrying out one or more successive linear combinations of p independent initial realizations, then composite realizations successively obtained possibly with new draws, etc., the coefficients of this combination being such that the sum of their squares is 1.
French Patent 2,795,841 filed by the assignee describes another method for gradually deforming the representations or realizations, generated by sequential simulation, of a non necessarily Gaussian stochastic model of a physical quantity z in a gridded heterogeneous medium in order to adjust them to a series of data relative to the structure or to the state of the medium, which are collected by prior measurements and observations. The method essentially comprises applying an algorithm allowing gradual deformation of a stochastic model to a Gaussian vector with N mutually independent variables, which is connected to a uniform vector with N mutually independent uniform variables by the Gaussian distribution function so as to define realizations of the uniform vector, and using these realizations to generate representations of this physical quantity z, which are adjusted in relation to the data.
The above methods are applicable to gridded models (pixel type models) suited for modelling continuous quantity fields and they are therefore ill-suited for modelling of zones crossed by fracture networks or channel systems for example.
Models based on objects are spatial arrangements of a population of geometrically defined objects. Basically, an object type model is a Boolean model that can be defined as a combination of objects identical by nature with a random spatial distribution. Boolean models (of object type) are of great interest for the geometric description of heterogeneous media such as meandrous deposit systems, fracture networks, porous media on the grain size scale, vesicle media, etc. Geologic objects are defined by their shape and size. Their location in the field is defined by taking account of their interactions: attraction-repulsion, clustering tendency, etc.
Unlike pixel type models, the models based on objects can provide for example realistic geologic representations of an underground reservoir at an early stage where the data obtained by in-situ measurement are still rare.
The prior art in the sphere of object type models is notably described in the following publications    Matheron, G., 1967, “Elément Pour une Théorie des Milieux Poreux”, Masson, Paris;    Matheron, G., 1975, “Random sets and Integral Geometry”, Wiley, New York;    Serra, J., 1982, “Image Analysis and Mathematical Geology”, Vol. I, Academic Press, London    Stoyan, D. S. et al., 1995, “Stochastic Geometry and its Applications”, 2nd Edition, Wiley, Chichester;    Lantuéjoul, C., 1997, “Iterative Algorithms for Conditional Simulations, in Baafi and others, eds.”; Geostatistics Wollongong 96, Vol. I, Kluwer Acad. Pubi., Dordrecht, The Netherlands, p. 27–40.
The position of the objects in an object type model is distributed according to the Poisson point process. The shape and the size of the objects are independent of their positions. This model can be generalized by a combination of objects of different nature and/or using a non-stationary density Poisson point process.
Although Boolean models have been widely studied in the literature, there is no coherent and efficient method for constraining these models to the physical data, notably hydrodynamic data, which is however a major challenge for their application to reservoir engineering. The methods allowing gradual deformation of pixel type stochastic reservoir models such as those described for example in the two aforementioned patents cannot be directly used for Boolean models. Constraining Boolean models to hydrodynamic data for example requires development of coherent algorithms for deformation and displacement of the objects.